Abstract
In this paper, we investigate the first and second Zagreb multiplicative indices of zero divisor graphs of reduced rings from an applied perspective. The zero-divisor graph of a ring, denoted by \(\Gamma (R)\), consists of non-zero zero-divisors of a ring R as its vertex set, with two vertices connected by an edge if their product is zero. Recently, in Selvakumar et al. (Discr Appl Math 311:72–84, 2022), we explored the Wiener index of the zero divisor graph under various conditions: (i) when R is a reduced ring, (ii) when R is the ring of integers modulo n, and (iii) more generally when R is the product of the rings of integers modulo n. This paper extends that work by examining the Zagreb multiplicative indices, another significant topological index, utilizing analytical methods. We provide explicit formulas for these indices specifically when the ring R is reduced. The applicability of these formulas is demonstrated through numerous examples provided.
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Communicated by S. Ponnusamy
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The corresponding author and she acknowledges the CSIR Junior Research Fellowship (09/0652(11961)/2021-EMR-I).
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Selvakumar, K., Gangaeswari, P. Some applications of multiplicative Zagreb index. J Anal (2024). https://doi.org/10.1007/s41478-024-00771-y
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DOI: https://doi.org/10.1007/s41478-024-00771-y